[gregorio]

It is very rare but now I have to correct you on a mistake. Countable infinite is a thing.

Ah yes, I stand corrected. However, if I’ve now understood the term correctly it doesn’t make any material difference to what I stated, real sounds are not comprised of a “countable infinite” number of sine waves/frequencies, we do not have “corresponding points” (to those countably infinite frequencies) in our basilar membrane and he would still need an infinite amount of time to physically count them all!

G

 

[Ryokan]

Me and many thousands like me are completely accustomed to audio gear/listening environments costing at a minimum several hundred thousand dollars and up to the tens of millions.

For places costing tens of millions are we talking opera houses?

 

[gregorio]

For places costing tens of millions are we talking opera houses?

No, Opera Houses don’t necessarily have any audio gear or even particularly good acoustics generally. I was talking about professional/commercial studios: commercial recording, mixing, mastering and re-recording (dubbing) studios/stages.

G

 

[gregorio]

Did you even listen to the first minute of what you yourself posted? Does “your science depth” not even go as far as being able to tell the difference between audiophile marketing BS and actual facts/science, really?

Have you ever heard a real instrument in your life?

No, none of us ever have, and that’s a truly remarkable achievement in my case. Have you any idea how difficult it is to formally train and then be a professional orchestral musician for over a decade without ever hearing a real instrument? Not easy as a recording engineer either!

[1] if you did maybe you will realize how unnatural these topping DACs and Amps sound. [2] But I dont think you are interested in understanding audio "science". [3] whatever makes you sleep better.

1. Err, DACs and Amps don’t produce any sound, so obviously we cannot realise how unnatural they sound!
2. While you apparently don’t even know what “audio” is, let alone understand any of the science of it!
3. It makes you “sleep better” to make-up numerous falsehoods, post them as fact in a science discussion forum and then get called out does it?

G

 

[castleofargh]

I do not know how does the small cochlea have anything to do with rel instruments, do you have any research paper about it ? but even if we cant record precisely the infinite sine waves, there is still varying levels of fidelity shown by different DAC in converting that not so faithful digital recording of limited bandwidth into analogue waves...again I cant prove this and nor can you. But I believe those thousands of people in the youtube comment sections and millions of audiophiles( many cant even hear till 20 khz as you said) more than those measurement chasers who might or might not have measured under ideal conditions...heck I see difference in chord mojo measurements between archimago's music,stereophile and audio science review forum...

https://archimago.blogspot.com/2022/01/review-measurements-chord-mojo.html

https://www.audiosciencereview.com/...-measurements-of-chord-mojo-dac-and-amp.5120/

maybe its because of poor electricity in amir's house, maybe its due to measurement rigs wizardry. As I said I cant prove it and nor can you, but I will take the word of millions of audiophiles.

As it is our capture mechanism for sound waves, I think that understanding the limitations of it can help bring fidelity expectations back to realistic levels instead of some philosophy that we always benefit from infinitely better with forever higher numbers everywhere.
I sort of hate you because it took me nearly an hour to find a working link for this:
https://journals.physiology.org/doi/full/10.1152/physrev.00044.2006
On the bright side, now I've saved it in PDF for safekeeping, so maybe I forgive you ^_^.

Just as a note, the more numerous hair cell type is given at around 11000. Adding the other type it's often rounded to about, 15000 (per ear) in papers and books. And even that number needs to be taken with some understanding of what role they may serve, because concerning hearing loss, I think it's accepted that we can have a third of those cells damaged in an area before a hearing test shows some loss of sensitivity (obviously the test itself isn't super precise, but it gives some idea about how perception is and at the same time isn't changed directly if a handful of those cells are not working). The potential for max level of detail where each cell tells us a little more about the details of the sound is evidently lost somewhere along the way. Otherwise, our experience of sound would readily be impacted by even a few damaged cells. We cannot act like idealistic audiophile scrutinizing audio gear while keeping some candid views of perfect and infinite human sensory ability.

Here is a cochlea. The frequencies marked are where the mechanical resonance is found for each, and as you can see between the 16kHz zone and the base (entrance, end of it on the left), is the area that will have to register every possible higher frequency. The higher the frequency, the shorter the wavelength and the closer to the entrance will be the resonance area (if the wave even manages to travel this far inside the body without losing too much energy).

I stole this from https://ujms.net/index.php/ujms/article/download/6251/12036

And as I said, for lower frequencies, the resonance is also a matter of wavelength and distance travelled in the cochlea, so the entrance also shakes. Not as strongly as the area where there is resonance, but still, all sounds pass through the entrance dedicated to pick up all the high frequencies. Pretty much everything is against those cells surviving over time and us having good sensitivity at high frequency.
And that's obviously an issue. For example, if we fail to perceive content beyond 20kHz, there will be no difference in our perception in that ear between an infinitely complex audio signal with huge frequency spectrum, and one that has been low passed to attenuate or remove the frequencies well above 20kHz. We do not need the infinitely complex music when we can't notice so much of that complexity.

And it's the same practical problem for amplitude. We don't notice changes of less than 0,1dB. We notice very quiet sounds only if there is no loud signal in a nearby frequency at the same time. We have a strict limit for the perception of dynamic. Every sensory variable shows a threshold when tested. By definition, we have limits everywhere and won't notice all the variations below those thresholds. So why should we be concerned with infinitely complex capture and playback of music. Give me something close to the limits of what I can notice, and I'll enjoy it just as well as the more accurate option.



All this is not an argument against your blind test or some gears effectively sounding different. As I said, it's all about thresholds and the actual magnitude of changes. Plus the quality of the listening experiment. You feel strongly about your own experience, like most people, and that's pretty normal. We on the other hand tend to put a confidence value on data, that is directly linked to the reliability of the method to acquire it. Meaning, it is hard to convince us with an online testimony of a not that rigorous listening test. I have no opinion about how different your devices sounds, I haven't tried. I do have an opinion, as I already mentioned, on how you conducted your blind test and on the necessity for precise volume matching.
About different measurements showing different values, that's normal. They didn't measure the same device, only the same model. They didn't use the same rig for measurements or same software. Some measurements have strict standards, some not so much, or people just don't follow the standards. Will they send the exact same voltage, use the same sample rate and test signal? So when people effectively measure different things, they can get different results. That's pretty logical.
And of course if we start measuring very small quantities, we will inevitably run into noises and inaccuracies. You could measure the very same thing twice in a row and find such tiny differences.
It just turns out that for a great many measurements, the levels of precision are one or more magnitude lower than our hearing threshold. The obvious exception being measurement of transducers, because when using a mic we inevitably introduce it as another transducer, and we also pick up all the noises in the room. So we can rapidly reach limits of accuracy that aren't necessarily higher than a guy with good listening skills.
For a DAC or an amp, I'd argue that the only reasons not to see the difference that is heard, is that A/ we didn't measure the right variable, or B/ it wasn't actually heard.

 

[MrHaelscheir]

One curiosity. So far, I have only seen linearity measurements of DACs, which I suppose makes sense as they are producing the analog signal in the first place rather than having the existing analog signal pass through with a transfer function. Is it possible for a DAC to measure linearly, but for other stages to introduce linear distortions audible as frequency response differences?

 

[bigshot]

Why wouldn't a simple null test give you the answer? Just take a track and capture the output of several DACs and null them against each other. That will tell you if one is different.

These folks always start arguing that digital audio imparts some sort of alteration to the sound; then when that is proven to be wrong, the start talking about the caps and analog out (as if it is a difficult thing to build a transparent RCA out jack!)

 

[VNandor]

It is very rare but now I have to correct you on a mistake. Countably infinite is a thing. It is a well defined concept in mathematics. A set is countably infinite if there exists a bijective function from the set of natural numbers to that set. And strangely enough, there also exists sets that are larger than countably infinite, like the set of real numbers. Very interesting subject by the way.

https://mathworld.wolfram.com/CountablyInfinite.html

As an example, an "ideal", non bandlimited square wave contains a countably infinite amount of harmonics. For every single harmonic, an integer number can be assigned but a finite amount of them is not enough for all of them.

I'm not sure if anyone cares or knows enough math to correct me but as far as I know, sounds either contain an uncountably infinite amount of harmonics or a finite amount of harmonics depending on how you define the function (sound pressure changes over time) that describes the sound/music. However, it can never have countably infinite amount of harmonics.

If the sound is transformed to the frequency domain by evaluating the fourier integral over a set amount of time, for example between t=0 and t=600 for a 10 minute long piece of music, you'll get a fourier series by definition. The fourier series gives the weight of discrete frequencies contained in the signal. The spacing of the discrete frequencies is determined by the the time window. In this case, the spacing would be 1/600Hz. From this, it can be seen that there's only a finite number of frequencies that can be crammed into a bandlimited signal (and sound is always bandlimited) because bandlimit is eventually reached by taking the 1/600Hz (or any non-infinitesimally small) steps.

If the sound is transformed by evaluating the integral from negative infinity to infinity, how the sound (piece of music) is defined must be decided explicitly since the sound only exists for a set amount of time. The typical thing to do is to say that the function is zero for all the time values where it would be otherwise undefined. So for 10 minutes of music that starts at t=0, the evaluated function would be zero from negative infinity to t=0 and it would zero again from t=600sec to infinity again. This "setting to zero" can be precisely described as the product between the 10 minute long music with a period time of 10 minutes and the appropriate boxcar/rectangular function which gets rid of the periodicity. This is the mathematical equivalent of "setting a function to zero" outside of a certain interval. This way the function is defined for all real values so the fourier transform can be properly evaluated from negative infinity to infinity.

This multiplication done in the time domain is the same as doing convolution in the frequency domain according to the convolution theorem and its inverse.

In essence, this equation states that the spectrum of the elementwise product between two signals is the same as the convolution of the two spectrums of the two signals. The spectrum of the music can be given by its fourier series and the spectrum of the rectangular function is the sinc function (which comes up suspiciously often when discussing audio). Since the sinc function is continuous and is defined for all real numbers, the convolution between the sinc and the spectrum of the music will also be defined for all real numbers. From this, the mapping between the real numbers and the points in the spectrum really sets up itself. It also means that the music defined this way will have an uncountably infinite number of harmonics.



The above might not make any sense for people not familiar with the concept of different infinities, the various fourier series and transforms and the convolution theorem but there can be a more hand-wavy way to look at this same problem. The first equation shows how to calculate the weights of the fourier series of g(t) and the second equation shows how to calculate the spectrum of g(t). They are remarkably similar at first glance.

In the first equation, P denotes the period time and n denotes the n-th harmonic. The equation gives the weights at every n/P frequencies. If there is no bandlimit, you have to calculate all the weights all the way up to the "infinitely high" frequencies. It doesn't matter if the frequency steps given by n/P is big, you'll always have to calculate the next weight because it's going to be non-zero. This would be the square wave case from earlier.
However, if the signal is bandlimited the bandlimit will be eventually be reached as long as the n/P step is not extremely small (as long as P doesn't approach infinity).

If P approached infinity in the first equation, you would get quite close to the second one which is the equation for the fourier transform. First, the signal would have to be integrated for "infinity". The bounds from the first equation could be rewritten to read as -P/2 to +P/2 which is really the same as 0 to P (the weights calculated from that would be the same) and the negative infinity to positive infinity could be reached that way, although 0 to infinity is just as infinite as negative infinity to infinity. Secondly, the n/P becomes smaller and smaller, and as P reaches infinity, it would become the continous variable "f" from the second equation. As f is continous, the transform will be defined for all real values which are of course, uncountably infinite. At that point the two equation would be (almost) the same. This line of thinking could be taken as far as saying that the fourier transform is just a special case of the fourier series, it's special because the period time is infinite and as such, it's more general than the series because it can be applied to non-periodic signals as well.

 

[MrHaelscheir]

With the receipt of my Lavricables Grand cable for my HE1000se purely as my favourite-looking option for a 4.4 mm termination, I have put together this video presenting my final findings stemmed from the measurements in this thread and https://www.head-fi.org/threads/con...les-mattering-for-audio.970430/#post-17816683 (post #8), partly to provide videographic proof of my actual ownership and measurement of these cables. More details and chapter timestamps are in the video description.